The paper considers the problem of robustness in hierarchical bayesian models. In specific we address Bayesian robustness in the estimation of normal means. We provide the ranges of the posterior means under $varepsilon$-contamination class as well as the density ratio class of priors. For the class of priors that are uniform over a specified interval we investigate the sensitivity as to the choice of the intervals. The methods are illustrated using the famous baseball data of Efron and Morris(1975).